Geometry

Question Analysis

The main focus is to apply the Pythagorean Theorem to find the length of the shortest route (the hypotenuse of a right - triangle) from the mountain back to the camp. Then, calculate the total distance Maria hiked by adding the lengths of all three segments of her hike.

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths  and  and hypotenuse of length , . In this context, the two legs of the right - triangle are the 10 - mile westward hike and the 24 - mile northward hike, and the hypotenuse is the return journey.

Step - by - Step Solution

1. Find the length of the return journey:

The lengths of the two legs of the right - triangle are  miles and  miles.

Using the Pythagorean Theorem .

Substitute the values: .

Calculate  and

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